Asymptotic behavior of Green's functions and correlation functions in the statistical theory of nonequilibrium processes

Expressions are obtained for the asymptotic Green's and correlation functions of arbitrary operators which are not integrals of the motion. The derivation of the expressions presupposes only the existence of a set of operators (coarse-grain variables) such that the variation in time of their mean values determines the slow evolution of the system. It is shown that the correlation functions of the coarse-grain variables, the fluxes, and their “random” components can be expressed in terms of the same transport coefficients. The nonequilibrium statistical operator method is used to derive dynamical equations with sources for the asymptotic Green's functions of the coarse-grain variables.